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1
Adjoint Shape Optimization Example #1
using OpenFOAM
- Target Velocity Profile at Outlet -
Fumiya Nozaki
Last Updated: 11 August 2014
English
Keywords:
• Continuous Adjoint
• Shape Optimization
• OpenFOAM
2
Optimization objective
Inlet
Outlet
Fixed velocity:
Parabolic profile
Fixed pressure
Target velocity profile
@ outlet:
Parabolic profile
Change shape to obtain
the target velocity
profile @ outlet
• Laminar flow
• Air @ 20℃
3
Objective function
𝐼 =
𝑐
2
𝒖 − 𝒖 𝑡𝑎𝑟𝑔𝑒𝑡
2
𝑑𝛤
𝑜𝑢𝑡𝑙𝑒𝑡
Difference between the calculated velocity and target velocity profile
Calculated by
simpleFoam
Target velocity
profile
Repeat shape modifications to get smaller value of 𝐼
Adjoint method gives
this information
4
Sensitivity map
Positive sensitivity area
⇒ Inward surface displacement
improves the objective
Sensitivity distribution
Negative sensitivity area
⇒ Outward surface displacement
improves the objective
5
Shape comparison between baseline and modified geometry
baseline modified
Shape
modifications
20 times
6
Outlet velocity distribution
baseline modified
Improved by 64%
7
Thank
You!

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